I think it's less of a question of if it's ok, and more of a question of do you have any other options?
Often when working on a project that spans the realms of both web and print, compromises and/or sacrifices are hard to avoid.
I'm working on marketing materials for a company that was founded long before the internet was a tool for businesses. They use a pretty old typeface in the logo and printed materials that is too distinctive to be replaced by any other system fonts.
Therefore, to achieve partial consistency on website headings, I found the absolute closest one I could on Google Fonts. My other option was to use Typekit and the exact font I wanted, but for various reasons that was not viable.
I won't use any more fonts; this is my absolute furthest compromise.
You shouldn't need more than two fonts for one branding element, as the second webfont should only be a compromise for the first print font.
Do not choose a different style of typeface just because you can't use the exact same one, use the closest fallback that you can find.
Now, if you have chosen two distinctive font styles, one for headings (serif) and another for body text (sans-serif) you might then need four in total; two primary print fonts and two almost identical fallback webfonts.
In most cases, two different fonts on one design is the most you should use.
Whether they know why or not, I assume the general public are subconsciously aware and have accepted that websites do not have as much of a diverse range of typefaces as print mediums.
My advice, evaluate all your options and then make a decision. Look at Typekit and see if their model is suitable for your project; if you feel it is, you should still look at Google Fonts just in case they have the same font for free.
To conclude, Yes it is acceptable to use two different - but as similar as possible - fonts for web and print, as long as you have truly evaluated all of your options against your project constraints.
If, after exploring your options you find that you can viably use the exact same font, it is your duty as a designer to achieve the greatest consistency that you're able to.